quadratic equations

Quadratic Equation Discriminant Proving Question

I realize many students have a challenge with presenting the solution of proving question. I am going to illustrate the correct way using the following question.

Show that is always positive for all real values of x.

=> what is always +ve? the values of y not x ( x can be of any values)

=> The graph will not touch x-axis; it is "hanging" above the x-axis

=> No roots, hence discriminant is less than 0

TIPS FOR SHOWING/PROVING QUESTION

Have an end in your mind. Be clear of the underlying concepts that the question is asking you to prove. Work towards that. For example, in the question, we want to prove that the discriminant is less than 0. <== this is the end.
Sketch to have a clearer idea.

Quadratic Equation And Discriminant

Click on picture for larger view

Siginifance of Discriminant $b^2-4ac$ : Type of Discriminant Determines The Types of Roots/Solutions ( No root, 1 real root or 2 real and distinct roots)

E-Maths Note: Quadratic Equations & Graphs Series Revisit

I have discussed about Quadratic Equations and Graphs previously in Features of Quadratic Equations and Graphs , Different representations of quadratic equations and their significance

This is really an important topic for students taking E-Math (elementary math) , more so for A-Math (additional math) as well.

Be sure that you know the basic of recognizing if a given equation is quadratic, how the quadratic equation looks like, the 5 main features of a quadratic graph, the different methods to solve a quadratic equation.

For students taking A-Math, you would definitely need to know more about the discriminant, sum or product of roots.

I would be elaborating more on methods to solve a quadratic equation and tips on discriminant so be sure you follow the blog by subscribing to the feed here.

E-Maths Note: Quadratic Equations & Graphs Series

For those in Sec 3s, you will be learning more about Quadratic Graphs. Not so much of the drawing like in Sec 2s, but more of indepth understanding.

A quadratic graph typically is either a smiley face :) or a sad face :( some prefer to call them U or n shape.

Q1: Do you know how to tell the "mood" of the quadratic graph given its equation? Be very speific to ensure crystal clear understanding.

Eg :) or :(

E-Maths Note: Quadratic Equations & Graphs

3 Different representations of a quadratic equation & its significance

: typical quadratic equation : Max/Min & instant answer to y-intercept
: Completed Squ form : Great for solving equation

: Instant answer to x-intercepts aka roots

Since we are on this topic of quadratic, one of the most important aspects is quadratic graphs.
There is a software which I use often for plotting of all sorts of graphs!
Yes, what you need to do is to "feed" the software with the equation of the graph that you intend to plot!

Get your free software for plotting by clicking here >>
Graphmatica Software

Now you know how your teachers plot their nice nice graphs :)